RT 5.2 Consider the differential: dp = dT + - ) dv (where a is a constant) (a) Determine whether the above differential, i.e. dp, is exact or not. Show all your steps and evaluation of the appropriate partial differentials!

Q: Let S be a linear transformation from R³ to R² with associated matrix Let T be a linear…

A: Let  be a linear transformation from  to  with associated matrix .Let  be a linear transformation…

Q: -4 Chapter 13 / Partial Derivatives f(x, y) = x2 + 2ry- 4x; P(1, 2), Q(1.01, 2.04)

A: Explained below

Q: 1. Explain why / f'(t) dt = f(b) – f (a). ||

A: Refer to image below.

Q: 0 6 417 8x dx ㅋㅋ 0 3,417 an ○ 2x-417dx 34/7) ㅊㅈ -417dx ○ 2x1017 dx

A:

Q: Find total differential of function u = x.

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A:

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A: According to the given information, Consider a family curve:

Q: 5

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Q: 3 b) Determine the derivative of - from First Principle. (5)

A: The derivative from first principle is given below. Hope this helps!

Q: V.EVALUATION: Given the following scores: 5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53, 65. Find: 1. Qi…

A: The given data is already in ascending order: 5,7,12,14,15,22,25,30,36,42,53,65 Q1=(n+1)4thterm…

Q: Consider this ordinary differential equation (ODE): dy da At the point (-0.5, 1.5), the direction…

A:

Q: For the function W= dw = - -8t ³ - 7t, express its differential, dw, as a function of t and at:

A: The function is given byTo determine: The expression of  as a function of  and .Formula Used :

Q: Linearize the following nonlinear differential equations for the input equilib- rium of u-2 9+uy-u.

A: 4.

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

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A:

Q: Consider the differential equation y' = 2y x a) Sketch the slope-field for x in [-2, 2] and y in [0,…

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Q: Determine which of the given differentials is/are exact. In case it is exact, find the functions of…

A: For a given differential A dx +B dy +C dz Where A,B,C are function of x,y,z  will be exact if for…

Q: (P-rule) 9. y=XN2X+ | %3D rewrite y

A: Given that:y=x2x+1

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A: As per the question we have to show the given relation between the derivative of the normal and the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.